A four-component clay-polymer-salt-water system, consisting of n-butylammonium vermiculite, poly-(vinyl methyl ether), n-butylammonium chloride, and heavy water, was studied by neutron scattering. The volume fraction of clay in the system and the salt concentration were held constant, at r = 0.01 and c = 0.1 M, respectively, and the volume fraction of polymer v was varied between 0 and 0.04. The addition of polymer, up to v = 0.04, had no effect on the phase transition temperature between the tactoid and gel phases of the clay system. However, even for v values as low as 0.001, the clay plates in the gel phase were more parallel and more regularly spaced than in the system without added polymer. In the gel phase, the lattice constant along the swelling axis of the clay colloid decreased exponentially as a function of the polymer volume fraction, from 12 nm at v = 0 to 8 nm at v = 0.04. In the tactoid phase, at T > 14 °C, the c-axis lattice constant in the crystalline regions was equal to 1.94 nm at v = 0 and 0.04, showing that the spacing between the clay plates is not affected by the added polymer when they are collapsed by an increase in temperature.